A circular wire loop of radius \( R \) is placed in the \( x-y \) plane centered at the origin \...

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A circular wire loop of radius \( R \) is placed in the \( x-y \) plane centered at the origin \( O \). A square loop of side \( a(aR) \) having two turns is placed with its center at along the axis of the circular wire loop as shown in figure. The plane of the square loop makes an angle of \( 45^{\circ} \) with respect to the \( z \)-axis. If the mutual inductance between the loops is given by \( \frac{\mu_{0} a^{2}}{2^{p / 2} R} \), then the value of \( p \) is
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